That depends on the structure and is a question for counsel rather than a default. Whichever party writes it, the letter needs to describe the professional duties, the terms of the arrangement, and its temporary nature consistently with the underlying contracts.
Make every document tell the same story
Inconsistency across an agency contract, a client statement, and a support letter is a common source of difficulty, because each was drafted for a different purpose. Compare job title, duties, duration, compensation, and worksite across all of them before anything is presented. Where they differ, have the discrepancy corrected at source rather than explained verbally later.
The first page should be the support letter, because it tells the officer what profession is claimed and why. A support letter that still shows the original end date invites questions no one can answer cleanly. Letters from past employers carry more weight than a resume because they state dates, position and duties from the source. Where the applicant will spend time at client sites, the letter should say who directs the work. The letter itself should state the job duties, the length of the assignment, the pay and the address where work will be performed.
Do not solve the conflict by quietly filing whichever translation fits better.